IGO 2018 A2

In acute triangle $ABC, \angle A = 45^o$ . Points $O,H$ are the circumcenter and the orthocenter of $ABC$ , respectively. $D$ is the foot of altitude from $B$ . Point $X$ is the midpoint of arc $AH$ of the circumcircle of triangle $ADH$ that contains $D$ . Prove that $DX = DO$ .

Proposed by Fatemeh Sajadi